Finite element analysis applied to cornea reshaping

Abstract

A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.

Noncontact Elastic Wave Imaging Optical Coherence Elastography for Evaluating Changes in Corneal Elasticity Due to Crosslinking

“…12) is similar to in situ measurements made by Brillouin spectroscopy [19]–[22]. Direct mechanical testing of different isolated layers of the cornea has shown that there is a large variation in mechanical properties between the anterior and posterior sections of the cornea [75],[76]. However, mechanical tests cannot be directly compared to the presented in situ tests as, for example, the “equivalent” IOP during uniaxial mechanical test is significantly higher [77].…”

Anterior and posterior corneal stroma elasticity after corneal collagen crosslinking treatment

“…These recordings were used to derive the sample’s force-indentation curves, after factoring out the cantilever deflection on a hard surface and incorporating the measured spring constant. With the use of custom MATLAB programs, the indentation force-indentation depth curves were analyzed using the Hertz model for a spherical indenter (Hertz H. 1881): $$F=\frac{4E\sqrt{R}}{3\left(1-{\nu }^2\right)}{D}^{3/2}$$where F [N] is the measured force (N), E [N/m 2 ] is Young’s modulus (Pa), ν is Poisson’s ratio (ν=0.49 for the cornea (Cabrera Fernandez et al 2005, Knox Cartwright et al 2011)), R [m] is the radius of the spherical indenter (m), and D is the measured indentation. These recordings were repeated at least 15 times per sample.…”

A Finite Element Model for Ultrafast Laser–Lamellar Keratoplasty

“…36 This will be another step in developing the model using 2D or 3D simulations to study lamellar refractive surgery when inhomogeneities in stiffness through the thickness are considered. 8,44 …”

“…To this end, a new biomechanical model that takes into account the stiffness variations throughout the thickness of the corneal tissue has been developed. 8,44 We should point out that the mesh density and the remaining input parameters must be the same as in the models presented here for a further comparison. The model would be able to provide a better prediction when compared to the clinical results.…”